Question

i will give 25 points

Answer 1

Answer:

2a²c = c²b + b²a

Step-by-step explanation:

Given Quadratic Equation is ax² + bx + c = 0.

Here, a = a, b = c, c = c.

Let α,β be the roots of the Quadratic equation.

(i) Sum of roots:

α + β = -b/a

⇒ α + β = -b/a

(ii) Product of roots:

αβ = c/a

⇒ αβ = c/a

Now,

Given that Sum of roots is equal to sum of squares of the reciprocals.

⇒ α + β = (1/α²) + (1/β²)

⇒ α + β = (α² + β²)/α²β²

⇒ (-b/a) = [(α + β)² - 2αβ]/(αβ)²

⇒ -b/a = (b²- 2ac)/c²

⇒ -bc² = ab² - 2a²c

⇒ 2a²c = c²b + b²a            

Hope it helps!                                                                                                                                                              

Answer 2

Answer:

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